Proof WritingMediumInduction ShareInduction · Medium problemInduction proves 11⋅2+12⋅3+⋯+1n(n+1)=nn+1\dfrac{1}{1\cdot2} + \dfrac{1}{2\cdot3} + \cdots + \dfrac{1}{n(n + 1)} = \dfrac{n}{n + 1}1⋅21+2⋅31+⋯+n(n+1)1=n+1n. In the step, kk+1+1(k+1)(k+2)\dfrac{k}{k + 1} + \dfrac{1}{(k + 1)(k + 2)}k+1k+(k+1)(k+2)1 must simplify to what?Akk+2\dfrac{k}{k + 2}k+2kBk+1(k+1)(k+2)\dfrac{k + 1}{(k + 1)(k + 2)}(k+1)(k+2)k+1Ck+1k+2\dfrac{k + 1}{k + 2}k+2k+1Dk+2k+3\dfrac{k + 2}{k + 3}k+3k+2Check Show answer Walk through it step by step Practice more like this Review this concept